Problem: Solve for $x$ and $y$ using substitution. ${-x-3y = -1}$ ${y = -x+3}$
Answer: Since $y$ has already been solved for, substitute $-x+3$ for $y$ in the first equation. ${-x - 3}{(-x+3)}{= -1}$ Simplify and solve for $x$ $-x+3x - 9 = -1$ $2x-9 = -1$ $2x-9{+9} = -1{+9}$ $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = -x+3}\thinspace$ to find $y$ ${y = -}{(4)}{ + 3}$ $y = -4 + 3$ $y = -1$ You can also plug ${x = 4}$ into $\thinspace {-x-3y = -1}\thinspace$ and get the same answer for $y$ : ${-}{(4)}{ - 3y = -1}$ ${y = -1}$